A mixed discrete-continuous fragmentation model
Motivated by the occurrence of “shattering” mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete-continuous fragmentation models. Once established, the model, which takes the form of an integr...
| Main Authors: | , |
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| Format: | Journal article |
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Elsevier
2018
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| _version_ | 1797080188020850688 |
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| author | Baird, G Suli, E |
| author_facet | Baird, G Suli, E |
| author_sort | Baird, G |
| collection | OXFORD |
| description | Motivated by the occurrence of “shattering” mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete-continuous fragmentation models. Once established, the model, which takes the form of an integro-differential equation coupled with a system of ordinary differential equations, is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato–Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve nonnegativity and conserve mass. |
| first_indexed | 2024-03-07T00:56:35Z |
| format | Journal article |
| id | oxford-uuid:8846cc5a-f2e8-4191-ae6b-c17721fc438e |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:56:35Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:8846cc5a-f2e8-4191-ae6b-c17721fc438e2022-03-26T22:16:11ZA mixed discrete-continuous fragmentation modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8846cc5a-f2e8-4191-ae6b-c17721fc438eSymplectic Elements at OxfordElsevier2018Baird, GSuli, EMotivated by the occurrence of “shattering” mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete-continuous fragmentation models. Once established, the model, which takes the form of an integro-differential equation coupled with a system of ordinary differential equations, is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato–Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve nonnegativity and conserve mass. |
| spellingShingle | Baird, G Suli, E A mixed discrete-continuous fragmentation model |
| title | A mixed discrete-continuous fragmentation model |
| title_full | A mixed discrete-continuous fragmentation model |
| title_fullStr | A mixed discrete-continuous fragmentation model |
| title_full_unstemmed | A mixed discrete-continuous fragmentation model |
| title_short | A mixed discrete-continuous fragmentation model |
| title_sort | mixed discrete continuous fragmentation model |
| work_keys_str_mv | AT bairdg amixeddiscretecontinuousfragmentationmodel AT sulie amixeddiscretecontinuousfragmentationmodel AT bairdg mixeddiscretecontinuousfragmentationmodel AT sulie mixeddiscretecontinuousfragmentationmodel |